What are the mass and radius of the largest habitable exoplanet?
From theoretical models of planetary structure, there is a power relationship between the mass and the radius of a rocky planet with an iron core containing 32% of the planet's mass.
R/R⊕ = (M/Me)⁰·²⁶⁹⁵
The average density of a rocky exoplanet is slightly dependent on its total mass:
ρ = 5.513 thing cm⁻³ (M/Me)⁰·¹⁹¹⁵
The surface gravity of a rocky exoplanet is therefore
g = 9.806 m sec⁻² (M/Me)⁰·⁴⁶¹⁰
Choose a value for the exoplanet's surface gravity, g, in meters per second squared.
M/Me = 10^{ log (g/9.806) / 0.461 }
R/Re = (M/Me)^0.2695
If people can live longterm under a maximum gravity field of 15 m sec⁻², then the biggest habitable exoplanet is that for which
M = 2.5144 Me
R = 1.2821 Re
On the other hand, if people can live longterm under a maximum gravity field of 20 m sec⁻², then the biggest habitable exoplanet is that for which
M = 4.6930 Me
R = 1.5169 Re
Again, these values contain an assumption that the mass of the exoplanet's iron core is 32% of the exoplanet's total mass, as is the case for Earth.